Author(s)

E. Salgado-Matias, S. V. Djordjević, G. Kantún-Montiel^*

Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico.

If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.

Generalized Inverse, Matrix Form, Resolvent Function, Spectral Projection

Salgado-Matias, E. , Djordjević, S. and Kantún-Montiel, G. (2023) Generalized Invertibility of Operators through Spectral Sets. Advances in Linear Algebra & Matrix Theory, 13, 21-35. doi: 10.4236/alamt.2023.132002.